octave-antonio: scripts/sparse/spaugment.m annotate

annotate scripts/sparse/spaugment.m @ 20164:df437a52bcaf stable

doc: Update more docstrings to have one sentence summary as first line. Reviewed miscellaneous, sparse, strings in scripts directory. * scripts/miscellaneous/bzip2.m, scripts/miscellaneous/citation.m, scripts/miscellaneous/compare_versions.m, scripts/miscellaneous/computer.m, scripts/miscellaneous/debug.m, scripts/miscellaneous/dir.m, scripts/miscellaneous/edit.m, scripts/miscellaneous/error_ids.m, scripts/miscellaneous/fileattrib.m, scripts/miscellaneous/fullfile.m, scripts/miscellaneous/genvarname.m, scripts/miscellaneous/gzip.m, scripts/miscellaneous/mkoctfile.m, scripts/miscellaneous/news.m, scripts/miscellaneous/open.m, scripts/miscellaneous/parseparams.m, scripts/miscellaneous/recycle.m, scripts/miscellaneous/run.m, scripts/miscellaneous/swapbytes.m, scripts/miscellaneous/tar.m, scripts/miscellaneous/tmpnam.m, scripts/miscellaneous/unpack.m, scripts/miscellaneous/what.m, scripts/sparse/bicg.m, scripts/sparse/bicgstab.m, scripts/sparse/cgs.m, scripts/sparse/colperm.m, scripts/sparse/eigs.m, scripts/sparse/etreeplot.m, scripts/sparse/gmres.m, scripts/sparse/gplot.m, scripts/sparse/ichol.m, scripts/sparse/ilu.m, scripts/sparse/pcg.m, scripts/sparse/pcr.m, scripts/sparse/qmr.m, scripts/sparse/spaugment.m, scripts/sparse/spconvert.m, scripts/sparse/spdiags.m, scripts/sparse/spfun.m, scripts/sparse/spones.m, scripts/sparse/sprandsym.m, scripts/sparse/spstats.m, scripts/sparse/spy.m, scripts/sparse/svds.m, scripts/sparse/treelayout.m, scripts/sparse/treeplot.m, scripts/strings/base2dec.m, scripts/strings/bin2dec.m, scripts/strings/blanks.m, scripts/strings/cstrcat.m, scripts/strings/deblank.m, scripts/strings/dec2base.m, scripts/strings/dec2bin.m, scripts/strings/dec2hex.m, scripts/strings/findstr.m, scripts/strings/hex2dec.m, scripts/strings/index.m, scripts/strings/isletter.m, scripts/strings/isstrprop.m, scripts/strings/mat2str.m, scripts/strings/ostrsplit.m, scripts/strings/regexptranslate.m, scripts/strings/rindex.m, scripts/strings/str2num.m, scripts/strings/strcat.m, scripts/strings/strchr.m, scripts/strings/strjoin.m, scripts/strings/strjust.m, scripts/strings/strmatch.m, scripts/strings/strsplit.m, scripts/strings/strtok.m, scripts/strings/strtrim.m, scripts/strings/strtrunc.m, scripts/strings/substr.m, scripts/strings/untabify.m, scripts/time/datenum.m: Update more docstrings to have one sentence summary as first line.

author	Rik <rik@octave.org>
date	Mon, 04 May 2015 14:22:02 -0700
parents	9fc020886ae9
children

rev	line source
19697 4197fc428c7d maint: Update copyright notices for 2015. John W. Eaton <jwe@octave.org> parents: 18809 diff changeset	1 ## Copyright (C) 2008-2015 David Bateman
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	2 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	3 ## This file is part of Octave.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	4 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	8 ## your option) any later version.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	9 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	13 ## General Public License for more details.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	14 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	16 ## along with Octave; see the file COPYING. If not, see
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	18
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	19 ## -- texinfo --
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	20 ## @deftypefn {Function File} {@var{s} =} spaugment (@var{A}, @var{c})
18809 53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	21 ## Create the augmented matrix of @var{A}.
53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	22 ##
53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	23 ## This is given by
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	24 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	25 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	26 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	27 ## [@var{c} * eye(@var{m}, @var{m}), @var{A};
4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	28 ## @var{A}', zeros(@var{n}, @var{n})]
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	29 ## @end group
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	30 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	31 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	32 ## @noindent
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	33 ## This is related to the least squares solution of
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	34 ## @code{@var{A} \ @var{b}}, by
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11523 diff changeset	35 ##
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	36 ## @example
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	37 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	38 ## @var{s} * [ @var{r} / @var{c}; x] = [ @var{b}, zeros(@var{n}, columns(@var{b})) ]
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	39 ## @end group
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	40 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	41 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	42 ## @noindent
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	43 ## where @var{r} is the residual error
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	44 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	45 ## @example
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	46 ## @var{r} = @var{b} - @var{A} * @var{x}
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	47 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	48 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	49 ## As the matrix @var{s} is symmetric indefinite it can be factorized with
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	50 ## @code{lu}, and the minimum norm solution can therefore be found without the
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	51 ## need for a @code{qr} factorization. As the residual error will be
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	52 ## @code{zeros (@var{m}, @var{m})} for underdetermined problems, and example
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	53 ## can be
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	54 ##
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	55 ## @example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	56 ## @group
14327 4d917a6a858b doc: Use Octave coding conventions in @example blocks of docstrings. Rik <octave@nomad.inbox5.com> parents: 14138 diff changeset	57 ## m = 11; n = 10; mn = max (m, n);
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	58 ## A = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],
8516 e2a179415bac doc fixes John W. Eaton <jwe@octave.org> parents: 7687 diff changeset	59 ## [-1, 0, 1], m, n);
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	60 ## x0 = A \ ones (m,1);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	61 ## s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	62 ## [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	63 ## x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	64 ## x1 = x1(end - n + 1 : end);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	65 ## @end group
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	66 ## @end example
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	67 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	68 ## To find the solution of an overdetermined problem needs an estimate of the
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	69 ## residual error @var{r} and so it is more complex to formulate a minimum norm
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	70 ## solution using the @code{spaugment} function.
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	71 ##
20164 df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	72 ## In general the left division operator is more stable and faster than using
df437a52bcaf doc: Update more docstrings to have one sentence summary as first line. Rik <rik@octave.org> parents: 19833 diff changeset	73 ## the @code{spaugment} function.
18809 53af80da6781 doc: Update documentation of sparse functions including seealso links. Rik <rik@octave.org> parents: 17744 diff changeset	74 ## @seealso{mldivide}
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	75 ## @end deftypefn
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	76
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	77 function s = spaugment (A, c)
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	78 if (nargin < 2)
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	79 if (issparse (A))
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	80 c = max (max (abs (A))) / 1000;
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	81 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	82 if (ndims (A) != 2)
11589 b0084095098e missing semicolons in script files John W. Eaton <jwe@octave.org> parents: 11587 diff changeset	83 error ("spaugment: expecting 2-dimenisional matrix");
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	84 else
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	85 c = max (abs (A(:))) / 1000;
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	86 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	87 endif
19833 9fc020886ae9 maint: Clean up m-files to follow Octave coding conventions. Rik <rik@octave.org> parents: 19697 diff changeset	88 elseif (! isscalar (c))
11472 1740012184f9 Use uppercase for variable names in error() strings to match Info documentation. Only m-files done. Rik <octave@nomad.inbox5.com> parents: 11471 diff changeset	89 error ("spaugment: C must be a scalar");
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	90 endif
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	91
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	92 [m, n] = size (A);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	93 s = [ c * speye(m, m), A; A', sparse(n, n)];
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	94 endfunction
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	95
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	96
8871 fb1c929dbbb7 tests vs. 64-bit indexing John W. Eaton <jwe@octave.org> parents: 8516 diff changeset	97 %!testif HAVE_UMFPACK
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	98 %! m = 11; n = 10; mn = max (m ,n);
11471 994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	99 %! A = spdiags ([ones(mn,1), 10*ones(mn,1), -ones(mn,1)],[-1,0,1], m, n);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	100 %! x0 = A \ ones (m,1);
994e2a93a8e2 Use uppercase 'A' to refer to matrix inputs in m-files. Rik <octave@nomad.inbox5.com> parents: 10549 diff changeset	101 %! s = spaugment (A);
7681 b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	102 %! [L, U, P, Q] = lu (s);
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	103 %! x1 = Q * (U \ (L \ (P * [ones(m,1); zeros(n,1)])));
b1c1133641ee Add the spaugment function David Bateman <dbateman@free.fr> parents: diff changeset	104 %! x1 = x1(end - n + 1 : end);
14363 f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	105 %! assert (x1, x0, 1e-6);
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks Rik <octave@nomad.inbox5.com> parents: 14327 diff changeset	106

Mercurial > octave-antonio

annotate scripts/sparse/spaugment.m @ 20164:df437a52bcaf stable